A study on the (2+1)–dimensional first extended Calogero-Bogoyavlenskii- Schiff equation

Chaudry Masood Khalique; Kentse Maefo; Chaudry Masood Khalique; Kentse Maefo

doi:10.3934/mbe.2021293

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 5: 5816-5835. doi: 10.3934/mbe.2021293

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A study on the (2+1)–dimensional first extended Calogero-Bogoyavlenskii- Schiff equation

Chaudry Masood Khalique ^{1,2,3
,
,},
Kentse Maefo ³

1.
International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa
2.
Department of Mathematics and Informatics, Azerbaijan University, Jeyhun Hajibeyli str., 71, AZ1007, Baku, Azerbaijan
3.
The African Institute for Mathematical Sciences (AIMS) of South Africa, 6 Melrose Road, Muizenberg, 7945 Cape Town, South Africa

Received: 23 March 2021 Accepted: 07 May 2021 Published: 28 June 2021

This article studies a (2+1)–dimensional first extended Calogero-Bogoyavlenskii-Schiff equation, which was recently introduced in the literature. We derive Lie symmetries of this equation and then use them to perform symmetry reductions. Using translation symmetries, a fourth-order ordinary differential equation is obtained which is then solved with the aid of Kudryashov and $ (G'/G)- $expansion techniques to construct closed-form solutions. Besides, we depict the solutions with the appropriate graphical representations. Moreover, conserved vectors of this equation are computed by engaging the multiplier approach as well as Noether's theorem.
- extended Calogero-Bogoyavlenskii-Schiff equation,
- Lie symmetries,
- Noether's theorem,
- Kudryashov's method,
- conservation laws
Citation: Chaudry Masood Khalique, Kentse Maefo. A study on the (2+1)–dimensional first extended Calogero-Bogoyavlenskii- Schiff equation[J]. Mathematical Biosciences and Engineering, 2021, 18(5): 5816-5835. doi: 10.3934/mbe.2021293

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Abstract

This article studies a (2+1)–dimensional first extended Calogero-Bogoyavlenskii-Schiff equation, which was recently introduced in the literature. We derive Lie symmetries of this equation and then use them to perform symmetry reductions. Using translation symmetries, a fourth-order ordinary differential equation is obtained which is then solved with the aid of Kudryashov and $ (G'/G)- $expansion techniques to construct closed-form solutions. Besides, we depict the solutions with the appropriate graphical representations. Moreover, conserved vectors of this equation are computed by engaging the multiplier approach as well as Noether's theorem.

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